8 problems

An equivariant spectrum is connective when its fixed point spectra are connective. Bohmann–Osorno's conjecture. Every connective equivariant spectrum arises from Bohmann and Osorno…

Tillmann's equivalence conjecture. The two infinite loop space structures on $\mathbb{Z}\times B\Gamma_\infty^+$ are equivalent.

A bipermutative category has additive and multiplicative symmetric permutative structures, with the multiplicative structure distributing over the additive one. A symmetric bimonoi…

Let $BoP\langle n\rangle_k$ denote the $k$th space in the Omega spectrum of $BoP\langle n\rangle$. Consider those spaces that are irreducible and have two-primary torsion-free homo…

Weak geometric version of the Curtis and Eccles conjectures. (i) The image of the first homomorphism is finite. (ii) For a path connected space $X$, the image of the second homomor…

Odd-primary characteristic conjecture. $S/\!/p^r,\alpha_1$ is a characteristic for $H\mathbb{Z}/p^r$.

An $E_{\infty}$ ring $G$-category is a $G$-category with an action by an $E_{\infty}$ operad pair $(\mathcal{P}_G,\mathcal{R}_G)$ whose multiplicative action extends from…

Let $\mathcal{A}rc$ be the arc operad, and let ${}^{\rm Fat}{\mathcal S}t{\mathcal{GT}ree}$ denote the stabilized fat graph operad. A suitable stabilization conjecture for the arc…